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On Polynomial Estimators of Frontiers and Boundaries

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  • Hall, Peter
  • Park, Byeong U.
  • Stern, Steven E.
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    Abstract

    Motivated by problems of frontier estimation in productivity analysis, and boundary estimation in scatter-point image analysis, we consider polynomial-based estimators of the edge of a distribution. Our aim is to develop methods for correcting polynomial-type estimators of bias, and for constructing simultaneous confidence bands for the data edge. We tackle this problem by first deriving large-sample approximations to distributions of polynomial-based edge estimators, and then developing algorithms for simulating from them so as to produce Monte Carlo approximations to the distribution of the difference between the true edge and its estimator. This involves applying representations for joint extreme value distributions. The majority of attention is focused on the parametric case, but nonparametric problems, where polynomial approximations are fitted locally, are also considered.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 66 (1998)
    Issue (Month): 1 (July)
    Pages: 71-98

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    Handle: RePEc:eee:jmvana:v:66:y:1998:i:1:p:71-98

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    Related research

    Keywords: Bias; confidence band; edge; envelope; extreme value distribution; image; productivity analysis;

    References

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    1. SIMAR , Léopold, 1995. "Aspects of Statistical Analysis in DEA-Type Frontier Models," CORE Discussion Papers 1995061, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Tsybakov, A.B. & Korostelev, A.P. & Simar, L., 1992. "Efficient Estimation of Monotone Boundaries," Papers 9209, Catholique de Louvain - Institut de statistique.
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    Cited by:
    1. Hall, Peter & Park, Byeong U., 2004. "Bandwidth choice for local polynomial estimation of smooth boundaries," Journal of Multivariate Analysis, Elsevier, vol. 91(2), pages 240-261, November.
    2. Jeong, Seok-Oh & Park, Byeong U., 2004. "Limit Distribution of Convex-Hull Estimators of Boundaries," Papers 2004,39, Humboldt-Universität Berlin, Center for Applied Statistics and Economics (CASE).
    3. Daouia, Abdelaati & Noh, Hohsuk & Park, Byeong U., 2013. "Data envelope fitting with constrained polynomial splines," TSE Working Papers 13-449, Toulouse School of Economics (TSE).
    4. U. Park, Byeong, 2001. "On estimating the slope of increasing boundaries," Statistics & Probability Letters, Elsevier, vol. 52(1), pages 69-72, March.
    5. Girard, Stéphane & Guillou, Armelle & Stupfler, Gilles, 2013. "Frontier estimation with kernel regression on high order moments," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 172-189.
    6. Martins-Filho, Carlos & Yao, Feng, 2007. "Nonparametric frontier estimation via local linear regression," Journal of Econometrics, Elsevier, vol. 141(1), pages 283-319, November.
    7. Daouia, Abdelaati & Girard, Stéphane & Guillou, Armelle, 2014. "A Γ-moment approach to monotonic boundary estimation," Journal of Econometrics, Elsevier, vol. 178(2), pages 727-740.
    8. Hwang, J. H. & Park, B. U. & Ryu, W., 2002. "Limit theorems for boundary function estimators," Statistics & Probability Letters, Elsevier, vol. 59(4), pages 353-360, October.
    9. Girard, Stéphane & Jacob, Pierre, 2008. "Frontier estimation via kernel regression on high power-transformed data," Journal of Multivariate Analysis, Elsevier, vol. 99(3), pages 403-420, March.
    10. Martins-Filho, Carlos & Yao, Feng, 2008. "A smooth nonparametric conditional quantile frontier estimator," Journal of Econometrics, Elsevier, vol. 143(2), pages 317-333, April.
    11. Cheng, Ming-Yen & Hall, Peter, 2006. "Methods for tracking support boundaries with corners," Journal of Multivariate Analysis, Elsevier, vol. 97(8), pages 1870-1893, September.
    12. Girard, Séphane & Jacob, Pierre, 2009. "Frontier estimation with local polynomials and high power-transformed data," Journal of Multivariate Analysis, Elsevier, vol. 100(8), pages 1691-1705, September.

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